[填空题]
Let $f(x)=x^{3}+3 x^{2}-9 x+k$. Part of the graph of f is shown below. The graph of f has a local maximum at A, a local minimum at B and a point of inflection at C.
1.1. Find $f^{\prime}(x)$ =a$x^2$+bx-c;a= ,b= ,c= .
1.2. Find $f^{\prime \prime}(x)$ =ax+b;a= ,b= .
2. Find the x -coordinate of the point of inflection at C.
x=- .
Given that f(-1)=14 .
3.1. Find f(0) = .
3.2.Hence, find the coordinates of the local maximum A(x,y) and justify your answer.
A(- , )
4.Write down in order from least to greatest f$^{\prime \prime}$(B),f$^{\prime}$(B),f(B).
